cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015289 Gaussian binomial coefficient [ n,4 ] for q = -4.

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%I A015289 #23 Sep 08 2022 08:44:39
%S A015289 1,205,55965,14107485,3625623645,927257668701,237435704507485,
%T A015289 60779845138496605,15559876852907031645,3983313338565919030365,
%U A015289 1019729183363623510391901,261050608944894743386831965
%N A015289 Gaussian binomial coefficient [ n,4 ] for q = -4.
%D A015289 J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
%D A015289 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015289 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015289 Vincenzo Librandi, <a href="/A015289/b015289.txt">Table of n, a(n) for n = 4..400</a>
%H A015289 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (205,13940,-223040,-839680,1048576).
%F A015289 G.f.: -x^4 / ( (x-1)*(256*x-1)*(64*x+1)*(4*x+1)*(16*x-1) ). - _R. J. Mathar_, Aug 03 2016
%t A015289 Table[QBinomial[n, 4, -4], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o A015289 (Sage) [gaussian_binomial(n,4,-4) for n in range(4,16)] # _Zerinvary Lajos_, May 27 2009
%o A015289 (Magma) r:=4; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%K A015289 nonn,easy
%O A015289 4,2
%A A015289 _Olivier Gérard_, Dec 11 1999